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Associated Press
In this combination of file photos, former Vice President Joe Biden speaks in Collier, Pa., on March 6, 2018, and President Donald Trump speaks in the Oval Office of the White House in Washington on March 20, 2018. Biden has formally joined the crowded Democratic presidential primary race with a goal to unseat Trump. (AP Photo/File)

SALT LAKE CITY — Just hours after Joe Biden posted a video announcing his 2020 bid for the White House Thursday, President Donald Trump took to Twitter.

“Welcome to the race Sleepy Joe,” Trump tweeted Thursday. “I only hope you have the intelligence, long in doubt, to wage a successful primary campaign. It will be nasty - you will be dealing with people who truly have some very sick & demented ideas. But if you make it, I will see you at the Starting Gate!"

Trump’s taunts might seem like business as usual coming from a president known for his pugnacious persona on — and off — of Twitter, and especially given the two-year feud between Trump and Biden which has involved mudslinging, name-calling and even verbal fisticuffs.

But Thursday's tweets were different, Trump advisers told Politico. The insults he chose revealed genuine respect — and concern — about Biden’s potential to win, they said.

Trump talked privately to aides about the threat Biden posed as early as last fall, a Republican strategist with direct knowledge of the interactions told Politico, asking, “How are we gonna beat Biden?”

Even when reassured Biden would never prevail over his more liberal opponents, Trump insisted, “But what if he does?”

“The candidates he doesn’t talk about, it’s a signal that he doesn’t take them seriously,” a Republican strategist told CNN.

“We have had a number of conversations about potential challengers, and Biden has been at the top of the list because of his polling numbers,” a Republican lawmaker who talks frequently with the president told CNN. “He is seen as one of the most difficult potential challengers because of his appeal to independents and his likable style.”

Matt Rourke, Associated Press
In this April 11, 2019, file photo, former Vice President Joe Biden takes part in a forum on the opioid epidemic at the University of Pennsylvania in Philadelphia. Biden has formally joined the crowded Democratic presidential primary race, declaring the soul of the nation at stake if President Donald Trump wins re-election. In a video posted on Twitter on Thursday, Biden focused on the 2017 deadly clash between white supremacists and counter protesters in Charlottesville, Virginia, noting Trump said there were "very fine people" on both sides of the violent encounter. (AP Photo/Matt Rourke)

Citing such concerns, a Republican strategist told Politico Trump sees Biden as the biggest threat in 2020.

Trump denied the characterization.

"I don't see Joe Biden as a threat. No, I don't see him as a threat. I think he is only a threat to himself," Trump told reporters earlier this month. "He's been there a long time. His record's not good. He'd have to run on the Obama failed record."

Despite Trump’s denial, of the 20 Democrats running for president, none has quite as much in common with Trump as Biden, Politico reported.

And, counterintuitively, it may be the two candidates’ similarities — rather than their differences — that make Biden such a threat to Trump in 2020.

Biden and Trump have similar strengths.

Biden and Trump are similar in age — Trump is 72, Biden in 76. Both have appealed to voters with a “raw, unscripted approach to politics,” according to Politico.

Both have proven their ability to appeal to blue-collar voters without a college education. These Americans were once staunch Democrats, but have increasingly migrated to the Republican Party.

In comparison with other candidates in the Democratic field, Biden is also uniquely capable of competing with Trump in the Rust Belt states of Wisconsin, Michigan and Pennsylvania that helped Trump win in 2016.

At the same time, Biden represents "a vestige of the Obama administration," according to Politico, which Trump has focused on as he compares his own presidency to that of his predecessor.

But Trump and Biden have similar weaknesses too.

Both candidates are famous for their loquaciousness — talking far more and far longer than their aides would like. “Both are prone to remarks that induce cringes even among their supporters,” Politico reported.

Both can be hot-tempered and easily drawn into petty fights.

For example, in March 2018, Biden told a crowd at the University of Miami that he would have “beat the hell out of Trump” if they were in high school, given the president’s crude remarks about women.

Trump responded that the former vice president “would go down fast and hard, crying all the way. Don’t threaten people Joe!”

Gene J. Puskar, Associated Press
In this March 6, 2018, file photo, former Vice President Joe Biden speaks at a rally in support of Conor Lamb, the Democratic candidate for the March 13 special election in Pennsylvania's 18th Congressional District in Collier, Pa. Biden has formally joined the crowded Democratic presidential primary race. (AP Photo/Gene J. Puskar, File)

The candidates also have struggled to maintain a strong track record with the same key constituency: women.

Trump has often used vulgar language to describe women, most famously epitomized by the Access Hollywood tape.

But Biden, too, has come under fire for his treatment of women, including several women who have come forward recently to accuse the former vice-president of inappropriate touching.

And, as Biden prepared for his presidential announcement, he called Anita Hill to express “his regret for what she endured” 28 years ago, when, as chairman of the Senate Judiciary Committee, he presided over the confirmation hearings in which she accused Clarence Thomas, then President George Bush’s nominee to the Supremre Court, of sexual harassment.

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The call seemed to backfire, The New York Times reported.

“I cannot be satisfied by simply saying, ‘I’m sorry for what happened to you,’” Hill, now a professor of social policy, law and women’s studies at Brandeis University, told The Times. “I will be satisfied when I know that there is real change and real accountability and real purpose.”

However, despite recent media attention on the allegations against Biden, recent polling shows that Biden sits atop the Democratic primary contest because of support from women.